Bayesian inference of high-dimensional, cluster-structured ordinary differential equation models with applications to brain connectivity studies
2017
We build a new ordinary differential equation (ODE)
model for the directional interaction, also called effective
connectivity, among brain regions whose activities are measured by
intracranial electrocorticography (ECoG) data. In contrast to
existing ODE models that focus on effective connectivity among only
a few large anatomic brain regions and that rely on strong prior
belief of the existence and strength of the connectivity, the
proposed high-dimensional ODE model, motivated by statistical
considerations, can be used to explore connectivity among multiple
small brain regions. The new model, called the modular and
indicator-based dynamic directional model (MIDDM), features a
cluster structure, which consists of modules of densely connected
brain regions, and uses indicators to differentiate significant and
void directional interactions among brain regions. We develop a
unified Bayesian framework to quantify uncertainty in the assumed
ODE model, identify clusters, select strongly connected brain
regions, and make statistical comparison between brain networks
across different experimental trials. The prior distributions in
the Bayesian model for MIDDM parameters are carefully designed such
that the ensuing joint posterior distributions for ODE state
functions and the MIDDM parameters have well-defined and
easy-to-simulate posterior conditional distributions. To further
speed up the posterior simulation, we employ parallel computing
schemes in Markov chain Monte Carlo steps. We show that the
proposed Bayesian approach outperforms an existing
optimization-based ODE estimation method. We apply the proposed
method to an auditory electrocorticography dataset and evaluate
brain auditory network changes across trials and different auditory
stimuli.
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